JEE Main 12 Jan 2019 Morning Question 2
Question: The area (in sq. units) of the region bounded by the parabola, $ y=x^{2}+2 $ and the lines, $ y=x+1,x=0 $ and $ x=3, $ is [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) 15/2
B) 17/4
C) 21/2
D) 15/4
Show Answer
Answer:
Correct Answer: A
Solution:
The shaded region represents the required area in the figure.
Required area $ =\int\limits_0^{3}{[(x^{2}+2)-(x+1)]dx=\int\limits_0^{3}{(x^{2}-x+1)}dx} $
$ =[ \frac{x^{3}}{3}-\frac{x^{2}}{2}+x ]_0^{3}=9-\frac{9}{2}+3=\frac{15}{2}sq. $ units
